Question

The circle below is centered at the point (4,1) and has a radius of length 2. What is its equation?

Answer 1

if (x0,y0) is the center point of a circle, then

(x - x0)^2 + (y - y0)^2 = r^2

the equation is (x-4)^2 + (y-1)^2 = 4

Answer 2

`(x-4)^(2)+(y-1)^(2) =4`

Explanation:

we know that

The equation of a circle in center radius form is equal to

`(x-h)^(2)+(y-k)^(2) =r^(2)`

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

`(h,k)=(4,1)`

`r=2\ units`

substitute

`(x-4)^(2)+(y-1)^(2) =2^(2)`

`(x-4)^(2)+(y-1)^(2) =4`